热环境中黏弹性功能梯度材料及其结构的蠕变

基于经典的对应原理, 将 Mori-Tanaka 方法等细观力学结果推广于定常温度环境下的黏弹性情形. 根据泊松比与时间呈弱相关的特点, 给出 Laplace 象空间中功能梯度材料的松弛模量和热膨胀系数, 并直接建立耦合热应变的多维黏弹性本构关系. 在此基础上, 求解黏弹性功能梯度圆柱薄壳在热环境中的轴对称弯曲蠕变变形问题. 考虑材料热物参数的温度相关性, 首先确定稳态温度场, 导出相空间中轴对称弯曲变形的解析解, 采用数值反演得到蠕变变形. 算例表明, 蠕变初期, 热环境的影响明显, 随着时间增加, 热应力松弛, 影响逐渐消失. 当圆柱薄壳受轴压时, 相比于两端固支, 两端简支的端部变形更加明显. 通过圆柱薄壳的轴对称弯曲求解, 给出体积含量呈任意分布的黏弹性功能梯度结构在热机载荷下的蠕变分析途径. 

CREEP BEHAVIOR OF VISCOELASTIC FUNCTIONALLY GRADED MATERIALS AND STRUCTURES IN THERMAL ENVIRONMENT

Based on classical correspondence principle,Mori-Tanaka and other micromechanical approaches are extended to treat the case of linear viscoelasticity in the constant thermal environment.The relaxation modulus and coefficient of thermal expansion of linearly viscoelastic FGMs are given directly in Laplace phase space,and multi-dimensional viscoelastic constitutive relation coupling thermal strain is constructed through considering the weak time-dependent feature of Poisson’s ratio.Following the above work,the problem of axial symmetrical bending of viscoelastic functionally graded circular cylindrical thin shells is solved.The steady temperature field is determined taking into account of the temperature dependence of thermal and mechanical parameters.The analytic solution is derived in phase space and the creep deflection is obtained by means of Laplace numerical inversion.It is shown that the thermal effect is obvious at initial creep stage,but abates with the increase of time due to the relaxation of the thermal stresses,and the constraint effect for hinged ends is more prominent than that of clamped ends on the deflection near ends when circular cylindrical thin shell is subjected to axial compression.It is expected to give the general approach to analyze the creep deformation of viscoelastic functionally graded structures with arbitrary distribution of volume content under thermal and mechanical loading by solving above problem of axial symmetrical bending.